Radiant energy collection

ABSTRACT

Disclosed are non-imaging systems and devices for collection and concentration of electromagnetic energy and particularly solar energy including one or more longitudinally-extending, generally trough-shaped bodies having curving inner reflective walls for concentration of energy from a relatively large entrance aperture toward a relatively small exit aperture. Solar energy concentrators of the invention include energy traps and collect and concentrate substantial amounts of direct solar energy, even at solstice, without substantial diurnal tracking.

i United States Patent Winston 1 Dec. 2, 1975 RADIANT ENERGY COLLECTIONPrimary E.raminerAlfred E. Smith [75] Inventor: Roland Winston, Chicago,Ill. Assistant Exammer Mlchael Attorney. Agent, or FirmMerriam,Marshall, Shapiro [73] Assignee: The University of Chicago, Chicago, &Klo

Ill.

22 Filed: Dec. 28, 1973 [571 ABSTRACT Disclosed are non-imaging systemsand devices for [211 App! 429l61 collection and concentration ofelectromagnetic encrgy and particularly solar energy including one or[52] U.S. Cl. 350/293; 126/271; 350/294 more longitudinally-extending,generally trough- [51 Int. Cl. G02b 5/10 shaped bodies having curvinginner reflective walls for [58] Field of Search 126/270, 271; 33l/94.5P; concentration of energy from a relatively large en- 350/288, 293,294, 299, 310, 190 trance aperture toward a relatively small exitaperture. Solar energy concentrators of the invention include [56]References Cited energy traps and collect and concentrate substantialUNITED STATES PATENTS amounts of direct solar energy, even at solstice,with- 980,505 1/1911 Emmet l26/271 out substam'al d'umal 24 Claims, 19Drawing Figures US. Patent Dec. 2, 1975 Sheet 1 of7 3,923,381

FIG.

Sheet 2 of 7 3,923,381

U .S. Patent Dec. 2, 1975 FIG.5

FIG. 4

U.S. Patent Dec. 2, 1975 Sheet 3 of7 3,923,381

US. Patent Dec. 2, 1975 Sheet 4 of7 3,923,381

US Patent Dec. 2, 1975 FIG. /2

Sheet, 5 0f 7 3,923,381

FIG/3 FIG/4 FIG/5 fi V I Patent Dec. 2, 1975 Sheet 6 of7 3,923,381

US. Patent Dec. 2, 1975 Sheet 7 of7 3,923,381

FIG. /7

RADIANT ENERGY COLLECTION BACKGROUND OF THE INVENTION The presentinvention relates generally to electromagnetic energy collection andmore particularly to devices useful in the collection and utilization ofradiant energy from solar and other sources.

The prior art has proposed numerous devices for detection ofelectromagnetic energy (e.g., infrared scanners, detectors of light fromhigh energy particles, and the like) and for collection of such energy(e.g., microwave antennas, solar collectors, and the like) and isparticularly rich in suggestions of systems for collection andutilization of solar energy.

Notwithstanding the voluminous proposals of the art, among the basic,and as yet inadequately resolved, problems inherent in the efficientutilization of solar energy are avoidance of energy loss throughre-radiation (i.e., energy conservation) and avoidance of intricate, andhence costly, apparatus for tracking the sun in its apparent dailymotion through the celestial sphere.

A typical attempt to solve solar energy conservation problems involvesproviding coatings on energy absorbing surfaces as well as elaborateinsulation of the particular trap employed for the utilization ofcollected energy. U.S. Pat. No. 3,277,884, for example, illustrates sucha scheme.

Another common manner of dealing with energy conservation involvesincluding in the collection scheme reflective or refractiveconcentration apparatus to permit collection of solar energy impingingupon a relatively large area and focusing of collected energy toward arelatively small area of utilization. Typical schemes proposing use ofreflector concentrators are illustrated in U.S. Pat. Nos. 1,814,897,3,200,820 and 3,217,702, for example. (Shadowing" effects encountered indisposing an energy utilization body in path of sunlight impinging uponreflectors are to some extent avoided through use of off-axisreflectors, as in U.S. Pat. Nos. 3,052,229, 3,613,659 and Tabor,Stationary Mirror Systems for Solar Collectors Solar Energy, Vol. II,No. 3-4, pp. 27 et seq. (1958)). Typical lens systems for solarconcentration are illustrated in U.S. Pat. No. 3,125,091 and Meinel etal., Physics Looks at Solar Energy Physics Today, Vol. 25, pp. 684 etseq. (1972). All of the mirroring and lens systems proposed above arebasically imaging systems wherein solar energy is reflected or refractedto a system focal point at which the concentrated energy is utilized forheating or power generation.

Among the solutions proposed for avoidance of diurnal solar tracking isthe provision of huge, but marginally efficient, mirrored surfaces suchas shown in U.S. Pat. No. 3,179,105.

None of the prior art systems has adequately solved the problems ofenergy conservation and solar tracking and, to a degree, solution of oneproblem often tends to enlarge the difficulties posed by the other. Thisis to say that systems permitting solar concentration by large factorsgenerally will require the most careful and frequent diurnal adjustmentsfor solar tracking. Conversely, systems requiring little or no diurnaladjustment generally provide lowest factors of concentration. Thus,Tabor, infra concludes that the maximum concentration available in astationary system (i.e., one re- 2 quiring only seasonal solar tracking)is on the order of 3 or 4.

Non-imaging light funnels having utility in collection of light fromhigh energy particles and having a greater concentration capacity thanimaging systems have been proposed by the inventor and his collaboratorsin earlier publications i.e., Review of Scientific Instruments, Vol.37,No.8, pp 1094-5 (1966), ibid., Vol. 39, No. 3, pp 419-20 (1968), ibid.,Vol. 39, No. 8, pp. 1217-8 0 (1968), and J. Opt. Soc. Am., Vol. 60, No.2, pp. 245-7 (1970). The inventor also noted the similarity between suchfunnels and the geometry of retinal cones in J. Opt. Soc. Am., Vol.61,No.8, pp. 1120-1 (1971 Basically, the above publications dealt withproposals for ideal, conical-shaped, light collectors which approach anfnumber equal to 0.5, a physically unrealizable limit for lens systems.The field of acceptance of conical collectors therein proposed may berepresented by a right circular cone having a gradually diminishing(over about 1) external boundary cut-off.

SUMMARY OF THE INVENTION According to the present invention anon-imaging system of exceptional efficiency is provided for thecollection and concentration of electromagnetic energy. comprehended bythe invention are longitudinally extending, generally trough-shapedcollection structures including opposed inner reflective surfaces whichfunction to guide and concentrate radiant energy impinging upon arelatively large entrance opening toward and if desired, through arelatively small exit opening at which there may be disposed a trap fordetection or utilization of the concentrated energy. Preferredembodiments of the structures of the present invention possess anelliptical conical field of acceptance exhibiting an extremely sharpexternal boundary cut-off.

It is contemplated that embodiments of the present invention may be mosteffectively employed in the collection and utilization of solar energyto provide for high energy concentration (and hence achievement of hightemperatures and optimal energy conservation) with minimal solartracking.

Further aspects and advantages of the present invention will becomeapparent upon consideration of the following description thereof,reference being made of the following drawing.

BRIEF DESCRIPTION OF THE DRAWING FIGS. 1 and 2 are schematicrepresentations of radiant energy collection troughs of the presentinvention.

FIG. 3 is a transverse sectional view taken along line 3-3 of FIG. 2.

FIG. 4 is a transverse sectional view of a straight sided collectiontrough.

FIG. 5 is a composite transverse sectional view of collection troughsincluding troughs of the invention.

FIG. 6 is a graphic representation of the field of acceptance of acollection trough as shown in FIGS. 1-3.

FIG. 7 is a comparative graphic representation of relative fields ofacceptance.

FIG. 8 is a cross sectional view of an alternative embodiment of theinvention.

FIG. 9 is a schematic representation of another alternative embodimentof the invention.

FIG. 10 is a sectional view taken along line 10-10 of FIG. 9.

FIG. 11 is a schematic view of an embodiment of the invention useful insolar energy collection.

FIG. 12 is a graphic representation of relative solar motions.

FIG. 13 is a variant form of FIG. 12.

FIG. 14 is a graphic representation of the acceptance of a collector ofthe invention in terms of optical direction cosines.

FIG. 15 is a graphic representation of relative solar motion compared tothe field of acceptance of a collection trough of the present invention.

FIG. 16 is a schematic view of a solar energy collector of the presentinvention.

FIGS. 17-19 are schematic views of radiant energy collectors of thepresent invention.

DETAILED DESCRIPTION FIG. 1 illustrates an embodiment of anelectromagnetic energy collector of the present invention including agenerally trough-shaped body having longtiduinally extending,substantially parallel, geometrically similar side wall elements l1, 11,the inner surfaces lla, 11a of which are of energy reflective material.As shown, wall elements 11, 11 taper from an entrance aperture 12 to anexit aperture 13. FIG. 2 illustrates a similar structure including endwall elements 14, 14 which preferably extend from opening 13 to opening12 and preferably also have energy reflective inner surfaces 14a, 14a.As discussed in greater detail later, provision of reflective side wallelements results in donation of optical properties approximatingprovision of a trough of infinite length.

The optical properties of collectors of the type shown in FIGS. 1 and 2are best illustrated through consideration of FIGS. 3, 4 and 5. In FIG.3 a preferred embodiment of a collector of the present invention is seento have an entrance aperture of a transverse dimension d,, an exitaperture of a transverse dimension d overall height L, an optical axisdesignated OA, and a half field of view, designated 6. The optical axisof the trough is defined by a line extending from the entrance apertureto the exit aperture, all points of which are equidistant fromrespective opposed edges of each of said apertures. The half field ofview of the trough of FIG. 3 is defined for the purposes of the presentinvention as the angle formed by the intersection of the optical axisand a straight line connecting an edge of one aperture with thelaterally opposed edge of the other.

A property common to all collectors of the invention is the collectorsfield of acceptance which is defined as that three dimensional fieldfrom within which radiant energy (rays) impinging upon a given point inthe plane of the collector entrance aperture will reach the exitaperture either directly or by way of one or more reflections from thecollector reflective surfaces. Put another way, rays generated withinthe field of acceptance of a collector and reaching the entrance planewill invariably reach the exit aperture and those rays generated outsidethe field will not.

For the purposes of the present invention, the shape ofa wall element 11as revealed by the transverse cross sectional view of the collector 10will be shown as the profile curve of the element. Accordingly, theprofile curve of a side wall element of a collector constructedaccording to the present invention may, for example, be anysubstantially smooth, non-convex line (connecting laterallycorresponding edges of exit and entrance apertures) falling within theshaded area of FIG. 5. It may be noted that the shaded area has as itsboundary but does not include a straight line as illustrated in the 4collector of FIG. 4. An included parabolic lineas shown in theembodiment of FIG. 3 forms the other boundary and is described ingreater detail hereafter. Concave curving lines of length greater thanthat of the above-mentioned parabolic line are also contemplated.

The profile curve of a much preferred embodiment of a collector of theinvention is shown in FIG. 3. The following aspects of that embodimentare of particular interest in understanding the invention.

1. The concentrative capability of the collector, i.e., the ratio ofexit aperture transverse dimension d to entrance aperture transversedimension d,, is equal to the sine of the half field of view (6) of thetrough.

2. The height, L, of the collector is equal to one-half the sum of d andd multiplied by the cotangent of the half field of view.

3. The profile curve of each wall element is a section of a parabolahaving as its focus the laterally opposed edge of the exit aperture andas its axis a line forming an angle with the optical axis of the troughequal to the half field of view (0) of the trough.

4. The embodiment accepts for concentration all energy deriving fromwithin an average elliptical conical field of acceptance developed bythe geometric accumulation of all elliptical conical field of acceptanceat all points within the plane of the entrance aperture, the parametersof each of said several fields being as follows (See FIG. 6):

a. The apex of the cone is any point, P, in the plane of the entranceaperture;

b. The axis of the cone is a line parallel to the optical axis of thetrough;

c. The semi-minor axis of the cone is in a direction transverse to thetrough. and subtends an angle equal to the half field of view (6) of thetrough; and

d. The semi-major axis extends in the longitudinal direction of thetrough and subtends an angle approaching (as the trough approachesinfinite length).

It will be noted that since the semi-major axis of the field ofacceptance at any point, P, approaches 90 for a collector of infinitelength, and since provision of reflective end walls donates opticalproperties approximating provision of an infinitely long trough, a crosssection (taken parallel to the plane of the entrance aperture) of theaverage field of acceptance of a collector as in FIG. 2 approximates theshape of an infinitely long rectangular strip. It follows that the areaof a sphere of unit radius intercepted by this field of acceptance (thesolid angle in steradians) approaches four times the half field of view(0), provided the angle 0 is measured in radians (one radian beingapproximately 57.3.

It is especially noteworthy that the field of acceptance of theembodiment is identical at each and every point, P, in the plane of theentrance aperture. This being the case, the field of acceptance is notsubject to failure or diminution at the edges of the collector troughand the maximum angle of acceptance within the field of acceptance ismeasured in a plane transverse to the collector, i.e., the angularacceptance of the entrance aperture, 0 of the collector isquantitatively equal to the angle of the half field of view (0).

Another property of interest in the embodiments of FIGS. l3 is thatradiant energy in the plane transverse to the trough which impinges atangles less than but closely approximating 0 with respect to the opticaxis are transmitted to the exit aperture with one or no reflections.

Further illustrative of such a collectors properties is the comparisonof its efficiency to that of a perfectly absorbing flat surface forisotropic radiant energy impinging on the entrance aperture at allangles up to 90 with respect to the optic axis. The ratio of energy persecond per unit area accepted by the collector to the energy per secondper unit area accepted by the absorbing surface is equal to thecollectors concentrative capability (the ratio of exit aperture width, dto entrance aperture width, d

In practice, numerous departures from the dimensional relationshipspresent in FIGS. 1-3 may be made in the construction of a collectorwhich will yield satisfactory, albeitrperhaps less than ideal, overallresults. For example, it may be noted that in FIG. 3 side wall 11terminates at a point wherein a line tangent to its parabolic curvaturewould lie parallel to the optical axis. It

may be desirable in some embodiments to provide a truncated collectiontrough having a height less than that of the collector of FIGS. 1-3 andin such cases side wall 11 would terminate short of the above-mentionedpoint.

It may be expedient to increase the overall height of the collector bylinearly extending reflective side walls 11a, 11a beyond the entranceaperture and parallel to the optic axis. Such virtual extension of theentrance aperture away from the exit aperture does not serve to alterthe angular acceptance of the collector but may diminish the collectorsefficiency because of resultant multiple reflections. It may further beexpedient to provide linear transition reflective wall segmentsextending away from the edges of the exit aperture, either parallel tothe optic axis or preferably tapering slightly outwardly, to accomodatetransmission of rays passing through the exit aperture toward aphotocell detector or the like.

Similarly, it is likely that a collector might be more economicallyfabricated in the form more closely approximating that illustrated incross section in FIG. 4. As might be predicted from known twodimensional analyses of optical collection properties of right circularcones (see, e.g., Williamson, Cone Channel Condenser Optics J. Opt. Soc,Am., Vol. 42, No. 10, pp. 712- (1952) and, White, Cone Channel OpticsInfrared Physics, Vol. 5, pp. 179-85 (1965)), a considerably morediffusely defined field of acceptance exists for such a structure, owingto the fact that the maximum angle of acceptance for given points in theplane of the entrance aperture is subject to variance depending uponrelative transverse distance from the optical axis of the trough. Thisfact may be best illustrated through consideration of the followinghypothetical example.

EXAMPLE I Assume the construction of a first collector according toFIGS. l3 wherein the ratio of d to d (and hence the concentrationfactor) is 9.6 and further that the half field of view equalsapproximately 6. The height (L) of the collector would be a fixeddimension according to the relationship described above, i.e., L ,5 (d dcot 0 The maximum angle of acceptance at all points in the plane of theentrance aperture would be equal to 6. In particular, radiant energyimpinging upon a point, P near the outermost edge of the entranceaperture would reach the exit aperture if it impinged upon P from anangle of less than about 6 6 in either direction measured transverselyto the trough optical axis.

Assume further the construction of a second collector of the formillustrated in transverse section in FIG. 4 having dimensions d,, d andL identical to those first of the collector. The collector would, ofcourse, provide the same theoretical concentration of isotropicallyimpinging energy but the field from which energy could be gathered wouldbe much less sharply defined. Energy impinging upon a point, P near theoutermost edge of the entrance aperture would be channeled to the exitaperture only if it impinged upon P from an angle of less than about 1measured transversely to the trough optical axis in one direction orless than about 11 from the opposite direction.

Use of straight or substantially straight side wall elements as in FIG.4 would give rise to acceptance of energy from marginal angles onlyafter multiple reflections with consequent energy loss due to absorptionby less than ideally reflective surfaces. The above example isschematically illustrated in FIG. 7.

While collection troughs of the invention preferably include smoothlycurving side walls, it is anticipated that some economic advantage infabrication might be derived through use of walls having one or moresegments revealed in profile curve as straight lines.

It is contemplated that space limitations may develop special utilityfor half trough structures as illustrated in a preferred embodiment byFIGS. 9 and 10 wherein the trough body 15 includes entrance and exitapertures l6 and 17, respectively, along with inwardly tapering sidewall element 18, a straight wall element 19 and, preferably, end wallelements 20, 20. Inner wall surfaces 18a, 19a and 20a would be radiantenergy reflective. In the embodiment illustrated, dimensionalrelationships maintained in fabrication are similar to those employed inconstruction of an embodiment according to FIG. 1-3, with expectedmodifications, i.e., entrance and exit apertures have one half thetransverse dimension, the half angle of view is the same, the length isthe same, the reflective surface 19a of wall element l9 lies along whatwould be the optical axis of a full trough, the focus of the paraboliccurvature of the side wall 18 is at what would be the opposite edge ofthe exit aperture for a full trough (shown in phantom lines), the axisof the parabola would form an angle with the optic axis equal to thehalf field of view and average field of acceptance would be anelliptical cone approaching an infinitely long rectangular strip intransverse cross section for an infinetely long collector.

FIG. 8 illustrates in cross section a tandem trough collector which,under circmumstances hereafter described, may provide greater factors ofconcentration than provided by a single trough. In the embodiment shown,there is a first trough 21 having respective entrance and exit apertures22 and 23, as well as side wall elements 24, 24 having energy reflectiveinner surfaces 24a, 24a. Contiguous to exit aperture 23 is a secondtrough 25 having an entrance aperture 26 of transverse dimension equalto aperture 23 and an exit aperture 27, as well as side wall elements28, 28 having energy reflective inner surfaces 280, 28a. Trough 21 isfilled with a medium having a refractive index, n, (e.g. air, which hasa refractive index of approximately 1.0), and trough 25 is filled with amaterial having a refractive index, n greater shown than n (e.g.,lucite, which has a refractive index of approximately 1.5).

In understanding the operation of the embodiment of FIG. 8, it should benoted that an energy concentrator of the type of collector FIGS. 13functions in part to reflect energy from within the collectors field ofacceptance to the exit aperture. In practice, some energy will directlyreach the exit aperture at an angle parallel to the optic axis of thecollector while, at the opposite extreme, some energy will reach theplane of the exit aperture at a grazing angle of nearly 90". To furtherconcentrate such grazing energy toward a tandem second collector exitaperture requires both the refractive capacity of a medium greater indexof refraction than that filling the first collector and an angular fieldof acceptance for the second collector equal to the critical angle ofits medium. With this in mind, the operation of a tandem collector willbe best understood through consideration of the following hypotheticalexample.

EXAMPLE II Assume one wished to concentrate radiant energy to thelongitudinally-extending photoelectric surface of an instrument having atransverse dimension d equal to 1 inch. Assume further that one wishedto concentrate energy from an angular field of acceptance of half angleequal to 16. To accomplish such a result one might construct a singletrough collector as shwon in FIGS. l-3 filled with a medium having anindex of refraction of 1. Since the exit aperture dimension is 1 inchand the desired maximum angle of acceptance is 16, the entrance aperturetransverse dimension and overall height of the trough may be derivedfrom the relationships heretofore described i.e., the ratio oftransverse exit aperture dimension to entrance aperture dimension equalsthe sine of the half field of view (which for the collector of FIGS. 1-3equals the maximum angle of acceptance), and, the overall height of thecollector equals half the sum of the entrance and exit aperturetransverse dimensions multiplied by the cotangent of the half field ofview. The transverse dimension of the entrance aperture would thus equal3.6 inches. The concentration factor of the collector would be equal to3.6.

One might instead construct a tandem trough collector as in FIG. 8wherein the first trough 21 was filled with a medium having an index ofrefraction, n of l, the second trough 26 was filled with a second mediumhaving an index of refraction, n of 1.5 and the photoelectric surfacewas in optical contact with the second medium. The maximum angle ofacceptance (critical angle) for trough 25 would be equal to the inversesine of the index of refraction of the medium filling trough 21 dividedby the index of refraction of the medium filling trough 26, i.e., arcsine n /n arc sine l/1.5 arc sine 0.6666 42. Given dimension d of exitaperture 27 equal to 1 inch and maximum angle of acceptance equal to 42,d the transverse dimension of the entrance aperture 26 would be equal to1.5 inches and the overall height would be 1.4 inches. With respect totrough 21, since the exit aperture 23 transverse dimension is equal to1.5 inches and the desired maximum angle of acceptance is equal to 16,the transverse dimension, d of the entrance aperture 22 would be 5.4inches and the overall height would be 12 inches. The concentrationprovided by trough 21 would be factor of 3.6 and the concentration ofthe entire tandem system would be equal to 1.5 times 3.6, or 5.4.

Finally, it may be noted that approximately the same concentration maybe derived through use of a single collector in optical contact with air(n, approximately equal to 1) at the entrance, but filled with a mediumof r1 1.5 and having 0 equal to 106 and other dimensions according tothe relationships above described.

According to another aspect of the invention, there are proposed systemsfor collection of solar energy which include radiant energycollector-concentrators as above described. The inherent attractivenessof directly using solar light to meet mans energy needs has motivated anintense search for practical solar power schemes. For most of these, itis necessary to concentrate the sun light by at least an order ofmagnitude in order to achieve high temperatures. This poses no problemin principle because the rays of sunlight are quite parallel (thehalf-angle 6, subtended by the solar disk is only lf) provided onetracks the suns location in the sky with an accuracy comparable to 6,.Because of the formidable technical problems associated with tracking tothis precision, it would clearly be an enormous advantage if therequired concentration was achievable by a relatively stationarycollector, i.e., one requiring little or no diurnal movement. Thispossibility was, in fact, explored in Tabor, infra, and thedisappointing conclusion was reached that the maximum possibleconcentration obtainable by a stationary collector was 3 or 4. Thisresult has been generally accepted to the present time. However, Taborsanalysis was based on conventional imaging optics and predated theinventors more recent developments which showed that systems thatcollect light but do not image can achieve a greater concentration thanimaging systems.

Inasmuch as it is desired to concentrate solar radiation with groundbased collectors, it is convenient for the purposes of discussing solartracking problems to adopt a Ptolemaic description of the suns motion inthe sky. To an adequate approximation, the apparent motion of the sun asviewed from a fixed point on earth, describes the cone depicted in FIG.12. In this figure the X axis direction is along north, the Y axisdirection along west and Z axis direction along the vertical. The coneaxis is in the X, Z plane, inclined at angle A, which is the latitude.The cone opening angle, a, is the angle between the earths axis ofrotation and the earth-sun direction. Since the earths axis is inclinedat an angle of approximately 235 with respect to the normal to the planeof its orbit (the ecliptic plane), the angle varies between theapproximate limits 66.5 s a g l l3.5 during the course of a year. Exceptat a time of equinox, when a a and the apparent solar path describes agreat circle wherein the sun does not rise or fall in the vertical, theproblem of collecting solar light is non-trivial and becomes mostdemanding at solstice (a 90 23.5). Collection and concentration of solarlight by high factors at the time of solstice for a reasonable fractionof the day, say 6 to 8 hours, may be considered the fundamental problemof solar collection. This is so because at such times the apparent riseor fall" in the vertical requires following or tracking the solar diskupwardly about 12 within the three or four hours prior to its reachingthe zenith (noon) position and downwardly" about another 12 within 3 or4 hours after its reaching the zenith position. Clearly, the stationarycollector which would continuously accept direct solar radiationthroughout the period of the above-mentioned il2 excursion during thetime before and after reaching the noon position,

and which further was capable of high orders of concentration,approaches the ideal in solar energy collection. The extent to whichcollectors of the invention approach this ideal is set forth hereafter.

10 Number of hours =2(/27T) (24) (dJ/fl') (24) where the factor 2results from the fact that Cosd is even in (b. Table I belowapproximates the number of accepted hours per day for a collector with19,, 6 (concentrafind that at the intersection of the two ellipses Cos[a 2a Sin 6,, (b Sin ]/[a (b Sin O 3 Therefore, the accepted number ofdaylight hours is given by The acceptance of a collector as shown inFIGS. 1-3 5 tion factor, 9.6) throughout the year in the approximamay bedescribed using optical direction cosines KX, tion of.a point-like sun.

TABLE I Collected hours Season 2T Cos 1 1 per day Equinox 0 (Full SolarEllipse Accepted) Full Daylight 0.37 68 9 30 0.57 55 7.4 Solstice 470.61 52.4 7.0

(See 14) were for i constant mdefx of Averaged over the year this givesapproximately 8 refraction, we may take K as the unit energy ray direcohours of collected sunlight. For 0 7 (concentration. KX, KY become tureHamiltonian variables contion factor of 8.2) one may obtain an averageday of apugate to X, Y when the light ray tra ectories are parameterizedb Z Here Z 's m sur d lo th 0 tic proxmately 9 hours of Sunhght' y 1 ea6 a mg 6 p Use of concentrator as in FIG. 8 which includes tanaxis ofthe collector. Hence I dXdY dKXdKY is Conserved dem trough collectorswherein n equals 1 and n Z =constant equals approximately 1.5 wouldresult in achieving 'In deriving the acceptance of such troughcollectors in concentration factors on the order of 12 to 15.

the KX, KY plane, the ray trajectories projected on a Table II, belowillustrates approximate concentration constant 'y plane behave as thoughthe collector were factors for collectors having 0 within the range oftwo dimensional, so that to 7 along with approximate totals of hours ofsunlight 2 h KX KKXZ K22) s smzo'm which may be collected at solstice(2T=47) 1n the ap- I KY x2 1 so th proximation of a point-like sun.

KX /(1 KY) s SinB KXlSinO s i KY2 TABLE II Kxzlsmzamu KY2 s l 9, 2T Cosl 1 Concentration Hours Thus the acceptance fills an ellipse ofsemi-minor axis Factor Collected equal to SinG and semi-major axis equalto 1, as 0567 555 82 shown in FIG. 14. 6 47 0.610 52.4 9.6 7.0 (It maybe recalled at this point that the collector 2, 1, 82 22-; u; 2concentrates by a factor of l/SinG or cosec 0 0:769 39:8 191 5:3 It iseasily shown that the apparent motion of the sun 0335 th KX K lane islso n 11' s A i nt 1 47 0912 m YP a e e P eohveh e way w 47 0.954 17.4ll4.6 2.3 to visualize this is to reconsider FIG. 12 and take as the Zdirection the zenith (highest point of the sun in the 40 y hoe") keepingthe direction west as It may be noted from the above that as the angularI acceptance of the collector diminishes, the concentrae yi e pfoleetloh0f the cone oh the X i Y tion factors increases and the number of hoursof sun- P giei 2 2: light which can be collected at solstice decreases.This a 2 E s 5 KY inherent property permits flexibility in solar energycolor, i terms f 2 a Si 2 s s 0 lection to fit the requirements of agiven environment COST s s eosT Hence, the semhminor axis E or a givenutilization scheme. Thus, when high tempera 1 2 1,5 s z and thesemhmajor i E b atures are desired, it may be preferable to employ aSiha cosT. small angular acceptance to achieve high concentra- FIG 15showS the ellipse described by the Sun on a tion even though a lessernumber of hours of sunlight solstice, the most difficult period forcollection. On the mlght he eoheeted solstice withoht diurnal move- Samefi has been added the acceptance f Si g ment. Alternatively, it may bedesirable to collect at 0.1 collector which concentrates the sunlight bya lower concentration for a longer average period of time factor 10.Clearly, such a collector accepts most of the and Such ease a largeraeeeptahee would be P useful day (7 to 8 hrs.) at solstice. Morerigorously, one ferredmust choose the axis to place the origin in the Itshould also be noted that variations in the profile plane at the centerf the collector ellipse o curve of collector side walls departing fromthat shown then finds that f the Solar ellipse in FIG. 3 may give riseto diminished, though still ad- 9, s X 5 Sin 0,, vantageous,concentrative capacity for a given angular H CST s KY s acceptanceand/or diminished, though still advantaf; MSW" 6 Sing 1 geous, timespans for collection of direct sunlight at solb cosT stice and/ordiminished, though still advantageous, Introducing a phase angle for thesolar ellipse, where total energy collection due to energy loss throughmu]- (1) 2 1r (=360) corresponds to the 24 hour day, we tiplereflections.

FIGS. 11 and 16 illustrate solar energy collection devices of thepresent invention which generally comprise one or morecollector-concentrator troughs as in FIGS. 1-3 and a solar energy trap.As used herein, the term trap includes any apparatus having a capacityfor accepting radiant energy of various wavelengths either for directutilization of such energy or as an intermediate in such utilization. Assuch, the term includes, but is not limited to, such direct utilizationdevices as photoand thermoelectric cells, as well as simple black bodycavities and variant cavity structures such as are disclosed in theNational Science Foundation publication NSF/RANN/SE/GI-34871/PR/72/4.

FIG. 1 1 shows a simple solar energy collector 29 with acollector-concentrator 30 as in FIGS. l-3 having contiguous to its exitaperture 31 a generally cylindrical energy receiving body 32 withcoaxial pipe 32 disposed therein. Pipe 33 may, for example, contain afluid to be heated by energy transmitted into cylinder 31 throughconcentrator 30. It is proposed the collector 29 may be disposed toextend longitudinally in an east-west direction and that suitable means(not shown) may be employed to rotate concentrator 30 and cylinder 31about pipe 33 for seasonal tracking of solar movement without disturbingthe orientation of pipe 33.

FIG. 16 illustrates a solar energy collector 34 including a plurality oflongitudinally-extending troughs 35 in edge to edge relationship withina box frame element 36. In the enclosed space 37 beneath troughs 35 isdisposed a coil element 38 in which a fluid may circulate forutilization of heat energy entering space 37 from troughs 35. Box frameelement 36 is preferably mounted with troughs 35 extending in aneast-west direction and the entire frame may be moved for seasonaltracking of solar movement.

It will be noted that for ease of fabrication it may be desirable toconstruct the trough inner side wall elements in the manner shown, i.e.,generally triangular elements 39 may be formed by extrusion (either ofreflective material such as aluminum or of a plastic material latercoated with a reflective material) to provide side wall surfaces 35a foradjacent troughs. A film 40 of a transparent material such as glass maybe disposed above troughs 35 for the purpose of protecting trough innerside wall surfaces 35a from dust and the like. Due to known selectivereflective properties (greenhouse effect), the use of an iron-free glassfilm may be particularly advantageous in selectively preventingre-radiation of infrared energy by reflecting a portion of reradiatedinfrared back toward its exit aperture source.

FIGS. 17-19 illustrate concentration devices useful in collection ofradiant energy deriving from within fields having a given angularity inone direction and a differing angularity in another. FIG. 17 (shown incross section in FIGS. 18 and 3) shows, for example a trough 42 of aconfiguration similar to that of FIG. 2, but wherein end wall elements43, 43 extend linearly from entrance aperture 44 for a given distanceand then taper toward exit aperture 45 to reveal a partially linear andpartially parabolic profile curve (See FIG. 18). FIG. 19 (shown in crosssection in FIGS. 18 and 3) shows a collector of a shape analogous tothat of an elliptic paraboloid but including parabolic inner surfacesdefined according to the relationships set forth above with respect toFIGS. 1-3.

Obviously many modifications and variations of the invention will occurto those of ordinary skill in the art and therefore only suchlimitations as appear in the appended claims should be applied thereto.

What is claimed is:

l. A non-imaging radiant energy concentrator, said concentratorcomprising:

a trough-shaped body having,

a longitudinally extending radiant energy entrance aperture with firstand second opposing edges separated by a transverse distance d alongitudinally extending radiant energy exit aperture, disposed oppositesaid entrance aperture, with first and second opposing edges separted bya transverse distance d a pair of symmetrical substantially concaveradiant energy reflecting and guiding side wall means interconnectinglaterally corresponding edges of said apertures,

a field of acceptance for radiant energy,

an angular acceptance for radiant energy within said field of acceptanceand determinable at said entrance aperture, and,

an optical axis determinable by reference to distances separatingentrance and exit aperture 0pposing edges,

' wherein the ratio of the distances d to dl is no less than the sine ofsaid angular acceptance, the profile curve of each of said wall means isa parabola having as its parabolic focus the opposing edge of said exitaperture and as its parabolic axis a line forming an angle with saidoptical axis of said body numerically equal to said angular acceptance,and the field of acceptance of the body, when represented in terms ofoptical direction cosines, is an ellipse of semi-minor axis equal to thesine of said angular acceptance and semi-major axis substantially equalto one.

2. A concentrator according to claim 1 wherein the distance separatingsaid apertures is no more than one half the sum of d and d multiplied bythe cotangent of said angular acceptance.

3. A concentrator according to claim 1 further including trough end wallmeans enclosing the space between by said energy reflecting and guidingside wall means.

4. A concentrator according to claim 3 wherein said end wall means areradiant energy reflective.

5. A concentrator according to claim 1 wherein said trough is filledwith a medium having an index of refraction greater than 1 and saidentrance aperture is in optical contact with a medium having an index ofrefraction lesser than that of the medium filling said trough.

6. A concentrator according to claim 1 further including a second suchtrough-shaped body disposed contiguous to said exit aperture, thetransverse distance separating first and second edges of the entranceaperture of said second trough body being identical to the transversedistance separating first and second edges of said exit aperture.

7. A concentrator according to claim 6 wherein said trough is filledwith a medium having a given index of refrection, said second trough isfilled with a medium having an index of refraction greater than that ofthe medium filling said trough, and the angular acceptance for energyrays entering the second trough is the inverse sine of the ratio of theindex of refraction of the medium filling the first trough to the indexof refraction of the medium filling the second trough.

8. A non-imaging radiant energy concentrator, said concentratorcomprising:

a trough-shaped body having,

a longitudinally extending radiant energy entrance aperture with firstand second opposing edges sepa- 13 rated by a transverse distance 11,,

a longitudinally extending radiant energy exit aperture disposedopposite said entrance aperture with first and second opposing edgesseparated by a transverse distance d a linear radiant energy reflectingand guiding side wall means interconnecting laterally correspondingfirst edges of said apertures,

a substantially concave, curving radiant energy reflecting and guidingside wall interconnecting laterally corresponding second edges of saidapertures,

a field of acceptance for radiant energy,

an angular acceptance for radiant energy within said field of acceptanceand dterminable at said entrance aperture, and,

an optical axis determinable by reference to distances separatingentrance and exit aperture opposing edges,

wherein the ratio of the distances d to d is no less than the sine ofsaid angular acceptance, the profile curve of said curving wall means isa parabola having as it parabolic focus a point, in the plane of saidexit aperture, spaced away from said' first edge of said exit aperture adistance equal to d and as its parabolic axis a line forming an anglewith said optical axis of said body numerically equal to said angularacceptance, and the field of acceptance of the body, when represented interms of optical direction cosines, is an ellipse of semiminor axisequal to the sine of said angular acceptance and semi-major axissubstantially equal to one.

9. A concentrator according to claim 8 wherein the distance separatingsaid apertures is no more than one half the sum of d and d multiplied bythe cotangent of said angular acceptance.

10. A concentrator according to claim 8 further including trough endwall means enclosing the space between said wall means.

11. A concentrator according to claim 10 wherein said end wall means areradiant energy reflective.

12. Solar energy concentration apparatus, said apparatus comprising:

a concentrator element including,

a pair of longitudinally extending substantially parallel walls havingsubstantially concave opposing inner solar energy reflecting surfaces,

each of said reflecting surfaces being sloped inwardly from an upperedge at an energy entrance aperture to a lower edge at an energy exitaperture, said exit aperture being of lesser transverse cross-sectionaldimension than said entrance aperture,

a field of acceptance for solar energy and an angular acceptance withinsaid field, determinable at said entrance aperture,

an optical axis determinable by reference to distances separatingrespective opposing upper and lower reflecting surface edges,

the profile curve of each of said reflecting surfaces being a parabolahaving as its parabolic focus the lower edge of the opposing reflectingsurface and as its parabolic axis a line forming an angle with saidoptical axis numerically equal to the angular acceptance of theconcentrator,

the dimensions of said apertures and the slope of said reflectingsurfaces being such that said field of acceptance is capable ofincluding an arc segment of coordinates equal to those described by theappar- 14 ent motion of the sun within at least one hour before andafter reaching zenith point at solstice; and,

a solar energy trap at said energy exit aperture.

13. Apparatus according to claim 12, wherein the height of saidconcentrator element is no more than one-half the sum of the transversecross-sectional dimensions of said entrance and exit aperturesmultiplied by the cotangent of said concentrator angular acceptance.

14. Apparatus according to claim 12 wherein the ratio of the transversecross-sectional dimensions of said concentrator element exit aperture tosaid entrance aperture is no less than the sine of said angularacceptance.

15. Apparatus according to claim 12 further including solar energyreflecting end wall means at the ends of said parallel walls of saidconcentrator element.

16. Apparatus according to claim 12 wherein said concentrator angularacceptance is 6.

17. Apparatus according to claim 12 wherein said concentrator element isfilled with a medium having an index of refraction greater than 1 andsaid entrance aperture is in optical contact with a medium having anindex of refraction less than that of the medium filling saidconcentrator.

18. Apparatus according to claim 12 further including a secondconcentrator element geometrically similar to said concentrator elementand disposesd between said concentrator element and said solar energytrap contiguous to said concentrator element exit aperture, thetransverse cross-sectional distance separating opposing upper edges ofsaid second concentrator element reflecting surfaces being identical tothe transverse cross-sectional distance separating opposing lower edgesof said concentrator element reflecting surfaces.

19. Apparatus according to claim 18 wherein said concentrator element isfilled with a medium having a given index of refraction, said secondconcentrator element is filled with a medium having an index ofrefraction greater than that of the medium filling said concentratorelement, and the angular acceptance for energy rays entering said secondconcentrator element is the inverse sine of the ratio of the index ofrefraction of the medium filling said concentrator element to the indexof refraction of the medium filling said second concentrator element.

20. Solar energy concentration apparatus, said apparatus comprising:

a concentrator element including,

a pair of longitudinally extending substantially parallel walls havingopposing inner solar energy reflecting surfaces,

one of said reflecting surfaces being substsantially concave and slopedinwardly from an upper edge at an energy entrance aperture to a loweredge at an energy exit aperture and the other of said reflectingsurfaces extending linearly from an upper edge at said energy entranceaperture to a lower edge at said energy exit aperture, said exitaperture being of lesser transverse cross-sectional dimension than saidentrance aperture,

a field of acceptance for solar energy and an angular acceptance withinsaid field, determinable at said entrance aperture,

an optical axis determinable by reference to distances separatingrespective opposing upper and lower reflecting surface edges,

the profile curve of said sloping reflective surface being a parabolahaving as its parabolic focus a point, in the plane of said exitaperture, spaced away from said linearly extending reflective surfacelower edge a distance equal to said exit aperture transversecross-sectional dimension and as its parabolic axis a line forming anangle with said optical axis of said concentrator numerically equal tosaid angular acceptance,

the dimensions of said apertures and the slope of said slopingreflecting surface being such that the field of acceptance of saidconcentrator is capable of including an arc segment of coordinates equalto those described by the apparent motion of the sun within at least onehour before and after reaching zenith point at solstice; and,

a solar energy trap at said exit aperture.

21. Apparatus according to claim 20 wherein the height of saidconcentrator elemenet is no more than the sum of the transversecross-sectional dimensions of said entrance and exit aperturesmultiplied by the cotangent of said concentrator angular acceptance.

22. Apparatus according to claim 20 wherein the ratio of the transversecross-sectional dimensions of said concentrator element exit aperture tosaid entrance aperture is no less than the sine of said angularacceptance.

23. Apparatus according to claim 20 further including solar energyreflective end wall means at the ends of said parallel walls of saidconcentrator element.

24. Apparatus according to claim 20 wherein said concentrator angularacceptance is 6.

Q PATENT NO. 3 923 3 1 DATED December 2, 1975 INVENTO I Roland Winstonare hereby corrected as shown below:

UNITED STATES PATENT OFFICE CETIFICATE OF CORRECTION It is certifiedthat error appears in the ab0veidentified patent and that said LettersPatent Col. 1, line 26, after "providing" insert selective Col. 3, line60, "shown" should be known Col. 4, line 26, "field" should be fieldsCol. 4, line 59, "is" should be as Q Col. 6, line 67 delete "shown".

Col. 8, line 65, "the" should be a Col. 9, line 18, "ture" should betrue Col. 9, line 45 and 46 before each line insert to designate themathematical "minus" quantity. Col. 9, line 60 should be Col. 10, line42, "factors" should be factor Col. 10, line 54, after "larger" insertangular Col. 12, line 7, "separted" should be separated Q Col. 12, line20, "dl" should be d Col. 12, line 57, "refrection" should be refractionCol. 13, line 14 "dterminable" should be determinable Col. 14, line 54,"substsantially" should be substantially Q Col. 16, line 2, "elemenet"should be element Signed and Scaled this thirteenth Day of A ttt'lr976[SEAL] O Arrest.-

RUTH C. MASON C. MARSHALL DANN Allvsn'ng Officer .(ummisxinnvr uflaremsand Trademarks O

1. A non-imaging radiant energy concentrator, said concentratorcomprising: a trough-shaped body having, a longitudinally extendingradiant energy entrance aperture with first and second opposing edgesseparated by a transverse distance d1, a longitudinally extendingradiant energy exit aperture, disposed opposite said entrance aperture,with first and second opposing edges separted by a transverse distanced2, a pair of symmetrical substantially concave radiant energyreflecting and guiding side wall means interconnecting laterallycorresponding edges of said apertures, a field of acceptance for radiantenergy, an angular acceptance for radiant energy within said field ofacceptance and determinable at said entrance aperture, and, an opticalaxis determinable by reference to distances separating entrance and exitaperture opposing edges, wherein the ratio of the distances d2 to d1 isno less than the sine of said angular acceptance, the profile curve ofeach of said wall means is a parabola having as its parabolic focus theopposing edge of said exit aperture and as its parabolic axis a lineforming an angle with said optical axis of said body numerically equalto said angular acceptance, and the field of acceptance of the body,when represented in terms of optical direction cosines, is an ellipse ofsemi-minor axis equal to the sine of said angular acceptance andsemi-major axis substantially equal to one.
 2. A concentrator accordingto claim 1 wherein the distance separating said apertures is no morethan one half the sum of d1 and d2 multiplied by the cotangent of saidangular acceptance.
 3. A concentrator according to claim 1 furtherincluding trough end wall means enclosing the space between by saidenergy reflecting and guiding side wall means.
 4. A concentratoraccording to claim 3 wherein said end wall means are radiant energyreflective.
 5. A concentrator according to claim 1 wherein said troughis filled with a medium having an index of refraction greater than 1 andsaid entrance aperture is in optical contact with a medium having anindex of refraction lesser than that of the medium filling said trough.6. A concentrator according to claim 1 further including a second suchtrough-shaped body disposed contiguous to said exit aperture, thetransverse distance separating first and second edges of the entranceaperture of said second trough body being identical to the transversedistance separating first and second edges of said exit aperture.
 7. Aconcentrator according to claim 6 wherein said trough is filled with amedium having a given index of refrection, said second trough is filledwith a medium having an index of refraction greater than that of themedium filling said trough, and the angular acceptance for energy raysentering the second trough is the inverse sine of the ratio of the indexof refraction of the medium filling the first trough to the index ofrefraction of the medium filling the second trough.
 8. A non-imagingradiant energy concentrator, said concentrator comprising: atrough-shaped Body having, a longitudinally extending radiant energyentrance aperture with first and second opposing edges separated by atransverse distance d1, a longitudinally extending radiant energy exitaperture disposed opposite said entrance aperture with first and secondopposing edges separated by a transverse distance d2, a linear radiantenergy reflecting and guiding side wall means interconnecting laterallycorresponding first edges of said apertures, a substantially concave,curving radiant energy reflecting and guiding side wall interconnectinglaterally corresponding second edges of said apertures, a field ofacceptance for radiant energy, an angular acceptance for radiant energywithin said field of acceptance and dterminable at said entranceaperture, and, an optical axis determinable by reference to distancesseparating entrance and exit aperture opposing edges, wherein the ratioof the distances d2 to d1 is no less than the sine of said angularacceptance, the profile curve of said curving wall means is a parabolahaving as it parabolic focus a point, in the plane of said exitaperture, spaced away from said first edge of said exit aperture adistance equal to d2 and as its parabolic axis a line forming an anglewith said optical axis of said body numerically equal to said angularacceptance, and the field of acceptance of the body, when represented interms of optical direction cosines, is an ellipse of semiminor axisequal to the sine of said angular acceptance and semi-major axissubstantially equal to one.
 9. A concentrator according to claim 8wherein the distance separating said apertures is no more than one halfthe sum of d1 and d2 multiplied by the cotangent of said angularacceptance.
 10. A concentrator according to claim 8 further includingtrough end wall means enclosing the space between said wall means.
 11. Aconcentrator according to claim 10 wherein said end wall means areradiant energy reflective.
 12. Solar energy concentration apparatus,said apparatus comprising: a concentrator element including, a pair oflongitudinally extending substantially parallel walls havingsubstantially concave opposing inner solar energy reflecting surfaces,each of said reflecting surfaces being sloped inwardly from an upperedge at an energy entrance aperture to a lower edge at an energy exitaperture, said exit aperture being of lesser transverse cross-sectionaldimension than said entrance aperture, a field of acceptance for solarenergy and an angular acceptance within said field, determinable at saidentrance aperture, an optical axis determinable by reference todistances separating respective opposing upper and lower reflectingsurface edges, the profile curve of each of said reflecting surfacesbeing a parabola having as its parabolic focus the lower edge of theopposing reflecting surface and as its parabolic axis a line forming anangle with said optical axis numerically equal to the angular acceptanceof the concentrator, the dimensions of said apertures and the slope ofsaid reflecting surfaces being such that said field of acceptance iscapable of including an arc segment of coordinates equal to thosedescribed by the apparent motion of the sun within at least one hourbefore and after reaching zenith point at solstice; and, a solar energytrap at said energy exit aperture.
 13. Apparatus according to claim 12,wherein the height of said concentrator element is no more than one-halfthe sum of the transverse cross-sectional dimensions of said entranceand exit apertures multiplied by the cotangent of said concentratorangular acceptance.
 14. Apparatus according to claim 12 wherein theratio of the transverse cross-sectional dimensions of said concentratorelement exit aperture to said entrance aperture is no less than the sineof said angular acceptance.
 15. Apparatus according to claim 12 furtheRincluding solar energy reflecting end wall means at the ends of saidparallel walls of said concentrator element.
 16. Apparatus according toclaim 12 wherein said concentrator angular acceptance is 6*. 17.Apparatus according to claim 12 wherein said concentrator element isfilled with a medium having an index of refraction greater than 1 andsaid entrance aperture is in optical contact with a medium having anindex of refraction less than that of the medium filling saidconcentrator.
 18. Apparatus according to claim 12 further including asecond concentrator element geometrically similar to said concentratorelement and disposesd between said concentrator element and said solarenergy trap contiguous to said concentrator element exit aperture, thetransverse cross-sectional distance separating opposing upper edges ofsaid second concentrator element reflecting surfaces being identical tothe transverse cross-sectional distance separating opposing lower edgesof said concentrator element reflecting surfaces.
 19. Apparatusaccording to claim 18 wherein said concentrator element is filled with amedium having a given index of refraction, said second concentratorelement is filled with a medium having an index of refraction greaterthan that of the medium filling said concentrator element, and theangular acceptance for energy rays entering said second concentratorelement is the inverse sine of the ratio of the index of refraction ofthe medium filling said concentrator element to the index of refractionof the medium filling said second concentrator element.
 20. Solar energyconcentration apparatus, said apparatus comprising: a concentratorelement including, a pair of longitudinally extending substantiallyparallel walls having opposing inner solar energy reflecting surfaces,one of said reflecting surfaces being substsantially concave and slopedinwardly from an upper edge at an energy entrance aperture to a loweredge at an energy exit aperture and the other of said reflectingsurfaces extending linearly from an upper edge at said energy entranceaperture to a lower edge at said energy exit aperture, said exitaperture being of lesser transverse cross-sectional dimension than saidentrance aperture, a field of acceptance for solar energy and an angularacceptance within said field, determinable at said entrance aperture, anoptical axis determinable by reference to distances separatingrespective opposing upper and lower reflecting surface edges, theprofile curve of said sloping reflective surface being a parabola havingas its parabolic focus a point, in the plane of said exit aperture,spaced away from said linearly extending reflective surface lower edge adistance equal to said exit aperture transverse cross-sectionaldimension and as its parabolic axis a line forming an angle with saidoptical axis of said concentrator numerically equal to said angularacceptance, the dimensions of said apertures and the slope of saidsloping reflecting surface being such that the field of acceptance ofsaid concentrator is capable of including an arc segment of coordinatesequal to those described by the apparent motion of the sun within atleast one hour before and after reaching zenith point at solstice; and,a solar energy trap at said exit aperture.
 21. Apparatus according toclaim 20 wherein the height of said concentrator elemenet is no morethan the sum of the transverse cross-sectional dimensions of saidentrance and exit apertures multiplied by the cotangent of saidconcentrator angular acceptance.
 22. Apparatus according to claim 20wherein the ratio of the transverse cross-sectional dimensions of saidconcentrator element exit aperture to said entrance aperture is no lessthan the sine of said angular acceptance.
 23. Apparatus according toclaim 20 further including solar energy reflective end wall means at theends of said parallel walls of said concentrator element.
 24. Apparatusaccording to claIm 20 wherein said concentrator angular acceptance is6*.